On the existence of subgame-perfect equilibrium in infinite-action games of perfect information

Abstract We study infinite-action games of perfect information with finitely or countably many players. It is assumed that payoff functions are continuous, strategy sets are compact, and constraint correspondences are continuous. Under these assumptions we prove the existence of subgame-perfect equilibria in pure strategies which are measurable functions. If for any date t , the subgame that is played from date t on depends on the history up to t only as this history affects some vector of “state” variables, then equilibrium strategies admit a “closed-loop” representation as measurable functions of the “state” trajectories.